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math-ph2025
On the Novikov problem for dihedral symmetry potentials
A. Ya. Maltsev
We consider Novikov's problem of describing level lines of quasiperiodic functions on a plane for two-dimensional potentials of dihedral symmetry. It is shown that quasiperiodic po…
math-ph2025
On the scaling properties of quasicrystalline potentials of eightfold rotational symmetry
A. Ya. Maltsev
We consider a special class of quasi-periodic potentials arising in the physics of photonic systems and possessing rotational symmetry of the 8th order. We are interested in the ``…
math-ph2025
On the level lines of two-layer symmetric potentials
A. Ya. Maltsev
We consider the behavior of level lines of two-dimensional potentials, which play an important role in the physics of ``two-layer'' systems. Potentials of this type are quasiperiod…